Universal Spacelikeness Estimates and Liouville Rigidity for Lorentzian $σ_k$ Curvature Equations

We study nonnegative entire spacelike graphs in Lorentz--Minkowski space satisfying $σ_k(A[u])=u^p$, with $h_{ij}=-Wu_{ij}$ and $W=(1-|Du|^2)^{-1/2}$. For $2\leq k<n$ and $p\geq k$, we establish bounds for the height and the Lorentz factor that depend only on $n,k,p$, assuming pointwise strict space